ABSTRACT
This chapter explores the power of even and odd, using twelve puzzles and a theorem. Puzzle topics included reproducing bacteria, chameleons, the missing digit in a power, diffie squares, and several hat puzzles. Some of the puzzles require consideration of a more general notion than parity: values modulo n, that is, the remainder of a number when divided by n. In the chameleon puzzle, a colony of chameleons contains 20 red, 18 blue, and 16 green individuals. When two chameleons of different colors meet, each of them changes his or her color to the third color. The reader is asked: Is it possible that, after a while, all the chameleons have the same color? The answer is that the difference between the number of individuals of any two colors remains the same modulo 3, and since none of those differences are 0 mod 3, the chameleons can never come down to just one color.
